Some of them did, albeit with a high amount of infant mortality thrown in. Consider the line of succession in the United Kingdom from Queen Anne downward:
| MONARCH | CHILDREN |
|---|---|
| Queen Anne | Seventeen pregnancies; all predeceasing her, dying in childbirth, or being lost to miscarriage. She is subsequently succeeded by her second cousin... |
| King George I | Five children between his wife and his mistress |
| King George II | Eight children |
| King George III | Fifteen children |
| King George IV | A single child -- a daughter. He is succeeded by his brother... |
| King William IV | Fathered fifteen children in all; ten with his mistress, five with his wife. Of his legitimate heirs, three were stillborn, one died shortly after being baptized, and one lived only a year. This led to a succession crisis, and so the crown passed to his niece... |
| Queen Victoria | Nine children; three would predecease her, and one (her eldest, also named Victoria) would die only months after the Queen herself |
| King Edward VII | Six children, one of whom lived for only a day |
| King George V | Six children, one of whom died as a child |
It is here that things take on their modern cast; Edward VIII did not reign long enough to produce any royal issue whatsoever, and George VI only had two daughters. As to why he and Elizabeth Bowes-Lyon didn't have more children than that, I can't say for sure. Nevertheless: the Seventh Lambeth Conference of 1930 was the first to declare birth control to be licit for couples who were communicants in the Church of England. Elizabeth had been born in 1926, and Margaret was born in 1930. It is possible that the royal couple took this newfound liberty to heart thereafter.
Miscarriages, stillbirths, and babies who died within a few hours, days, or weeks of life were unbelievably common in the pre-modern world. Although your question didn't mention a certain time period, speaking as someone relatively familiar with the medieval and early modern periods, there also tended to be different views about how often people regularly had sex. In the case of royal families, there was a common mindset that once you had "an heir and a spare," (or two male children) there was no need to continue having sexual relations (at least within the marriage) and many women chose to stop having sex because of the extremely high risks childbirth posed. There also used to be more deeply entrenched beliefs than today about when it was appropriate to have sex, and to what purposes. So, for example, no sex on Sundays, Wednesdays, and sometimes Fridays, no sex during Lent, no sex on certain religious holidays. There were also rules (although there is no way for historians to ascertain how closely people followed these) about how many times you could have sex per week, month and year, and about how much time needed to elapse between your last sexual encounter and the next time you would enter a church or holy place. Sex with menstruating women, pregnant women, women who had just given birth, and women who were breastfeeding was also frowned upon and discouraged. During some time periods, it was also believed that couples should only have sex with procreation in mind, so a form of the rhythm method was practiced and intercourse was only attempted when it was believed conception was most likely. The answer seems to be that while fetal, infant, and child mortality were extremely high, all in all people generally had less sex, and more focused procreative sex, than the average person might today.
Other people have talked about infant mortality, but there were sometimes other factors at stake - first, when you have an arranged marriage, you can be paired with a person whom you personally dislike or find unattractive. So you do your royal obligation to make an heir, and no more.
Second, lots of them were gay, or just uninterested in women.
Third, especially with the more inbred rulers, insanity and impotence were severe problems as well.
Sex with Kings and Sex with the Queen go into all these interesting stories.